Malmquist Indexes of Productivity Change in Tunisian Manufacturing Industries

This research aims to investigate the extent and nature of productivity growth in manufacturing industries using nonparametric frontier techniques. In order to decompose the total factor productivity (TFP) into technical efficiency change and technological change we use the output-oriented Malmquist productivity index method for 34 Tunisian manufacturing industries over the period 2002–2016. The results indicated that TFP has witnessed an average growth of two percent over the period 2002–2016. The productivity growth identified was attributed to the improvements in the technology (or frontier-shift) rather than improvements or changes in the efficiency.


Introduction
Since Solow's pioneering work, many theoretical and empirical studies have tried to analyze the factors explaining economic growth. Most of these studies concluded that productivity growth is the key to sustained economic growth. (See, among others, [1][2][3][4].) There are two basic approaches used for the measurement of productivity change: The econometric techniques based on the estimation of a production, cost, or some other functions, and the construction of index numbers using non-parametric methods. The initial technique is an explicit function assigned to the production possibility curve which carries out predictions of its parameters using econometrics which utilize empirical inputs and outputs. The technical efficiency outcome is dependent on the functional form which is taken, which if misstated may lead to outcome bias.
The other technique brings out the proposition that aims at finding out the over-all dynamic productivity transformation indices, which uses the data envelopment analysis (DEA)-based productivity index of Malmquist technique. Most methods advocate for a breakdown into two items; one to find out how efficiency has changed-this is indicated by any motion towards the production possibility curve. The other one indicates a change in the technology of the possibility frontier curve.
The aim of this paper is to develop an output based non-parametric methodology using the Malmquist productivity index methods for calculating productivity growth and to apply it to a sample of Tunisian manufacturing industries. The methodology adopted in this study includes the ideas from measurement of efficiency by [5,6].
There are a number of techniques that can be used to measure the level of productivity change. Productivity measures can be classified into single factor productivity measures (measure of output to a single measure of input); and multifactor productivity measure (measure of output to multiple measures of input) [25]. Single factor productivity measures usually include labor or capital; and multifactor productivity measures include capital and labor, or capital, labor, and intermediate inputs like services, energy, materials, etc. [26]).
The Malmquist index (MI) has gained popularity for measuring productivity change in recent years. A number of studies have shown the effectiveness of the technique in measuring productivity change (Grifell-Tatjé and Lovell [27]). It has also been identified that in the presence of non-constant returns to scale, the Malmquist productivity index does not accurately measure productivity change.
Accordingly, addressing various issues associated with MI, [28] proposed a new way for constructing MI in a global framework which makes use of the lowest level of extrapolation principle on the aggregation of the experienced contemporaneous technologies. It was also found by Pastor and Lovell [29] that the mean MI is not circular and adjacent period components have different measures in productivity change. The authors proposed that a global MI index happens to be circular and gives a single measure of productivity change. A number of studies have been done to implement MI in various international companies.
Other researchers [30] used MI approach for evaluating total factor productivity change across microfinance institutions in the Middle East and North America by investigating 33 institutions and found that overall productivity change was in regress and identified a decline in technological change. Coelli and Rao [14] utilized the DEA approach to find out the MI for evaluating the total factor productivity growth in agriculture across over 93 countries from 1980 to 2000. The shadow prices and value shares that are implicit in the DEA-based Malmquist productivity indices were also derived in the study. Ray and Desli [31] considered various aspects including productivity growth, technical progress, and efficiency change in industrialized countries using MI measures. Similarly, [32] considered a single context of the textile industry on an international scale for measuring the productivity changes using MI from 1995 to 2004 and found only a slight increase in productivity. These studies used MI on a wide scale at an international level or a group of countries, while also limiting to a specific industry, reflecting the wide-scale applicability of MI for measuring productivity, technology, and efficiency change.
Similarly, MI is also used in studies focusing on a particular sector specific to a region or a country which reflected the significant findings. Pharmaceutical and hospital industries in Sweden [33] are used for evaluating productivity developments in recent years. Similarly, they investigated the growth of Norwegian banks' productivity within the years 1980-1989, reflecting the applicability of MI for measuring productivity during environmental (economic/social/political) changes. Similarly, Price and Weyman-Jones [34] identified a significant increase in the productivity growth of the UK gas Sustainability 2020, 12, 1367 4 of 20 industry before and after privatization. Accordingly, MI approach is used for measuring productivity changes/growth across various industries, microfinance institutions in Kenya [35], Malaysian cage fish farming [36] road transport infrastructure in Spain [37], and Nigerian seaports after reform [38], reflecting the applicability of MI approach across various industries.
In the context of Tunisia, there are very few studies found using the concept of MI approach for measuring productivity changes across various sectors. Two studies were identified focusing on the evaluation of productivity changes across the Tunisian schools and educational institutions [39][40][41][42][43]. Zrelli and Belloumi [44] used MI for investigating the impact of environmental strategies on the Tunisian manufacturing industry during 1994-2008 by using data from 26 industries and found an average increase of 1.5% a year. Similarly, technical change and total factor productivity growth in the Tunisian manufacturing industry was evaluated by Kalai and Helali [26] by using data from six industries. They found that the industry achieved poor technological progress rates, and the efficiency gain observed was attributed to improvements in the technology. They observed that the total factor productivity improvement was on an average of 1.93% a year. The research in this area of the Tunisian manufacturing sector is very limited as only two studies were identified in the literature search. Considering these factors and the enhanced applicability of MI approach, this paper investigates productivity change in the Tunisian manufacturing industry.

Methodology
This study applies the DEA method and computes the Malmquist index to measure Tunisian's manufacturing productivity. However, the Malmquist index is demarcated using functions of distance that can be both input and output distance functions. An input distance function depicts the production technology by observing the comparative reduction of the input vector, given an output vector (Coelliet al., 2003). The function of output distance which reflects a maximum proportional expansion of the output vector, given an input vector is an issue that was recognized in this study. To describe the output distance function, a sample of K industry by x t ∈ R N + inputs in the production of x t ∈ R N + outputs in time dated t = 1, . . . , T is well-thought-out. Multiple inputs and outputs production technology may be defined using the output possibility set, P, which denotes the set of all outputs vectors,y t = (y t 1 , y t 2 , . . . , y t m ), which can be formed using the input vector, x t = (x t 1 , x t 2 , . . . , x t m ) through period t = 1, . . . , T. That is: P t x t = y t : x t can produce y t at time t t = 1, . . . , T Output oriented distance which is also referred to as distance function (Shephard (1970)) is described as follows: . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: The distance function is equivalent or less than 1 (i.e., D (x, y) ≤ 1), if and only if output y belongs to the production possibility set of x (i.e., y ∈ P (x)). Note that distance function is equivalent to the unit (for instance, D (x, y) = 1) if y belongs to the frontier of the production possibility set. An industry is considered technically effective if the interval function is correspondent to 1. Now for any given industry in period t, an output-based measure of efficiency can be presumed by the vertical distance ratio ob/oa. The outputs can be increased to make production technically efficient in time t (i.e., movement against the efficient boundary) as shown in Figure 1. By comparison, in vertical distance ratio oe/od in order to realize similar technical efficiency to that originates in time t. Since the frontier has shifted, od/oe exceeds unity, even though it is technically inefficient when compared to the period t + 1 frontier. The MPI measures the total factor productivity (TFP) change between two periods. MPI may be described using an output-oriented method or the input-oriented method. In this study we use the output oriented MPI. Output-orientation refers to the emphasis on the maximum level of outputs that could be produced using a given input vector and a given Sustainability 2020, 12, 1367 5 of 20 production technology relative to the observed level outputs. Following , the output oriented MPI between period t (the reference period) and period t + 1 is given by: Sustainability 2020, 12, x FOR PEER REVIEW 5 of 22 Now for any given industry in period t, an output-based measure of efficiency can be presumed by the vertical distance ratio ob/oa. The outputs can be increased to make production technically efficient in time t (i.e., movement against the efficient boundary) as shown in figure 1. By comparison, in vertical distance ratio oe/od in order to realize similar technical efficiency to that originates in time t. Since the frontier has shifted, od/oe exceeds unity, even though it is technically inefficient when compared to the period t + 1 frontier. The MPI measures the total factor productivity (TFP) change between two periods. MPI may be described using an output-oriented method or the input-oriented method. In this study we use the output oriented MPI. Output-orientation refers to the emphasis on the maximum level of outputs that could be produced using a given input vector and a given production technology relative to the observed level outputs. Following , the output oriented MPI between period t (the reference period) and period t + 1 is given by: MPI is a value in Equation (3). The first ratio signifies the time t Malmquist index and evaluates productivity change from period t to period t + 1 using period t technology as reference. The second ratio represents the period 1 + t Malmquist index and measures productivity change from period t to time t+1 using time t+1 technology as a reference. Notice that Equation (3) is the geometric mean of first and second ratios. Value of the , +1 ( , +1 , , +1 ) greater than unity will show positive TFP growth between two periods, whereas a value less than 1 specifies TFP deterioration. According to Färe and al. (1993), the MPI may be decomposed into two components that is an equivalent way of writing this productivity index (Equation(3)) as: Subscript 0 shows an output-orientation. The notation D t O x t+1 , y t+1 represents the distance function from the period t + 1 observation to the period t technology.
MPI is a value in Equation (3). The first ratio signifies the time t Malmquist index and evaluates productivity change from period t to period t + 1 using period t technology as reference. The second ratio represents the period 1 + t Malmquist index and measures productivity change from period t to time t+1 using time t + 1 technology as a reference. Notice that Equation (3) is the geometric mean of first and second ratios. Value of the M t, t+1 O x t , x t+1 , y t , y t+1 greater than unity will show positive TFP growth between two periods, whereas a value less than 1 specifies TFP deterioration. According to Färe and al. (1993), the MPI may be decomposed into two components that is an equivalent way of writing this productivity index (Equation(3)) as: In this equation the fraction outside the bracket ∆TE t, t+1 = D t+1 calculates the shift in the output-oriented of Farrell technical efficiency over the two periods.
The ratio in the square bracket TC t, t+1 = calculates the change in technology over the two periods. It is the geometric mean of the change in technology measured at time periods t and t + 1, assessed at x t and also x t+1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the  , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: time periods t and t + 1, assessed at and also +1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output. MPI in the mathematical Equation (4) Subject to: technology over the two periods. It is the geometric mean of the change in technology measured at time periods t and t + 1, assessed at and also +1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output. MPI in the mathematical Equation (4) comprises four different distance functions D O t (x t , y t ); D O t (x t+1 , y t+1 ); D O t+1 (x t , y t ) and D O t+1 (x t+1 , y t+1 ) . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: The ratio in the square bracket =[ +1 ( +1 , +1 ) +1 ( , ) ] calculates the change in technology over the two periods. It is the geometric mean of the change in technology measured at time periods t and t + 1, assessed at and also +1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output. MPI in the mathematical Equation (4) comprises four different distance functions D O t (x t , y t ); D O t (x t+1 , y t+1 ); D O t+1 (x t , y t ) and D O t+1 (x t+1 , y t+1 ) . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: In this equation the fraction outside the bracket ∆ = ( , ) calculates the shift in the output-oriented of Farrell technical efficiency over the two periods.
The ratio in the square bracket calculates the change in technology over the two periods. It is the geometric mean of the change in technology measured at time periods t and t + 1, assessed at and also +1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output. MPI in the mathematical Equation (4) comprises four different distance functions D O t (x t , y t ); D O t (x t+1 , y t+1 ); D O t+1 (x t , y t ) and D O t+1 (x t+1 , y t+1 ) . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: In this equation the fraction outside the bracket ∆ , +1 = +1 ( +1 , +1 ) ( , ) calculates the shift in the output-oriented of Farrell technical efficiency over the two periods.
The ratio in the square bracket calculates the change in technology over the two periods. It is the geometric mean of the change in technology measured at time periods t and t + 1, assessed at and also +1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output.
MPI in the mathematical Equation (4) comprises four different distance functions D O t (x t , y t ); D O t (x t+1 , y t+1 ); D O t+1 (x t , y t ) and D O t+1 (x t+1 , y t+1 ) . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: , +1 ≥ ⅄ ⅄ ≥ 0 Sustainability 2020, 12, x FOR PEER REVIEW 6 of 22 In this equation the fraction outside the bracket ∆ , +1 = +1 ( +1 , +1 ) ( , ) calculates the shift in the output-oriented of Farrell technical efficiency over the two periods.
The ratio in the square bracket calculates the change in technology over the two periods. It is the geometric mean of the change in technology measured at time periods t and t + 1, assessed at and also +1 . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output.
MPI in the mathematical Equation (4) comprises four different distance functions D O t (x t , y t ); D O t (x t+1 , y t+1 ); D O t+1 (x t , y t ) and D O t+1 (x t+1 , y t+1 ) . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output.
MPI in the mathematical Equation (4)  . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output.
MPI in the mathematical Equation (4) comprises four different distance functions . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: . Bigger than unity values for the ratios recommend improvement or values less than 1 recommend the contrary. Efficiency change ratio here denotes the enhanced capability of an industry to implement the global technology offered at different time points whereas technical change calculates the consequence of shift in the production frontier resulting from technological advances on industrial output.
MPI in the mathematical Equation (4)  . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: Y t+1 . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: . Following , and granted that suitable panel data are available, we can calculate these four functions by using DEA linear programs. For each industry, we calculate four distance functions to calculate TFP change between two periods t and t + 1. This requires the solving of four linear programming (LP) problems. Assuming constant returns-to-scale, to begin with, the following output-oriented linear programs are: where: y it and y i,t+1 are M × 1 vectors of output quantities for the i-th industry in period t and in period t + 1, respectively; x it and x i,t+1 are K × 1 vectors of input quantities for the i-th industry in period t and in period t + 1, respectively; Y it and Y i,t+1 are N × M matrixes of output quantities for all N industries in period t and in period t + 1, respectively; X it and X i,t+1 are N × K matrixes of input quantities for all N industries in period t and in period t + 1, respectively; is a N × 1 vector of weights; and θ is a scalar indicating the technical efficiency score. It's good to note that the first two linear programs five and six (LP (5) and (6)) are where the technology and the observation to be evaluated from the same period, and the solution value is less than or equal to 1. The linear programs seven and eight (LP (7) and (8)) occur where reference technology is developed in a one period from the data, whereas the observation to be evaluated is from another period. The parameter θ should not be greater than or equal to 1, since it should be calculating standard output-oriented technical efficiencies. The data point could lie above the production frontier. Statistically it may lie directly above the construction boundary. This can maximum in LP (8) the point of production from time 1 + t is as compared to technology in an advance epoch. However the technical developments have come about, then a value of theta less than 1 is feasible. This could also likely occur in LP (7) if technical regress has happened, however this is less likely. For this research, we have utilized the DEA methods to estimate the frontier functions and a data envelopment analysis computer program (DEAP) version 2.1 developed by Coelli (1996) for calculation of Malmquist TFP indexes.

Results and Discussion
The data used in this study consist of annual observations of 34 Tunisian manufacturing industries (see Table 1 & Appendix A) for which observations are available over the whole period 2002-2016. The industries included in the study are distributed in six sectors as follows: We note that the industries are distributed as follows across sectors: 26% belong to agriculture and food products (IAF), 12% to the construction materials, ceramics, and glass (CMCG), 24% to the mechanical and electrical industries (MEI), 15% to the chemical industry (CI), 12% to the textile, clothing, and leather industry (TCL), and 12% to other manufacturing industries (OMI).
The data contain data on input and output. We specify variable of yield and incoming variables. Our yield is the cost bought with a market price that is constant. Technology of production is defined as presumptuous of the regular scale of returns: Stock capital and input due to labor is measured for some permanent employees. Statistically they are assembled using a diversity of sources: The general organization of records as well as the quantitative economic system institution, allowing for the construction of an incorporated database. It is worth noting that even though the exertions market became more flexible over the complete duration, the public law for hours worked did now not trade. We expect that the level and the evolution of productivity have been now not raised by using these missing information Pham The capital stock has been calculated, at constant prices, using the perpetual inventory method for annual investment flows. This method defines the evolution of the capital stock at constant prices as follows: Where K t is the capital inventory at the instant t; K (t − 1) is the capital inventory on the spot t −1; I t is the funding on the instantaneous t; standard deviation which is a capital depreciation rate.
We have taken into consideration a mean 10% depreciation per year. Our foremost explanation for depreciating prices and productiveness fluctuations never proved to be weighty depreciation charges, as well as the concerned fact absence of the components. Table 2 shows descriptive statistics of input variable (L). The number of permanent employees increased by 52.5% on average between 2002 and 2016. However, on a year to year base, we observed small changes in the average number of permanent employees. On average, our statistics show an increase in the capital stock during the observed time period by 7.75% (see Table 3). The reason for the increase in capital stock is that some industries have changed from old to new equipment during the period 2002 and 2016. Our estimation of value added at constant market prices shows an increase by 83.27% between 2002 and 2016. However, we observe a remarkable increase of 14% between 2007 and 2008 (see Table 4).  (Coelli (1996)). We have thousands of pieces of information on the efficiency scores and peers of each industry in each year. We also have measures of technical efficiency change, technical change and TFP change for each industry in each pair of adjacent years. Tables 5-7 display the results. Table 5 suggests calculated modifications in relative output performance for every individual enterprise and the overall average for all industries. In an output-based model of productiveness exchange quite a value, more than regress value. But, in Tables 5-7, we think that improvement in productiveness, as well as improvement in efficiency and time, is indicated by using values greater than 1, while costs less than 1 indicate regress. We are also aware that the mode of LP (l) turned into selected output industry outcome.
The values in Table 5 constitute the period of time not within the Equation (4)' brackets, for instance changes in competence. For a company that is competent for time t + 1 and for time t maintains its performance relativity. No industry was green in all periods. For the nine industries four, five, eight, nine, 11,15,26,33, and 34, we discovered intervals with declines in performance in addition to periods with upgrades in performance. We discovered no industry with most effective development or only regress in performance at some point of the period 2002 to 2016. For the industries as an whole, five periods confirmed common development in performance, and in nine intervals there was decline in the mean performance. Within the years 2008 and 2009 the total fall in competence is 4.37%. This was observed through a 1.5%development in performance. We checked for minimal changes during the final periods. The bigger shifts inside the frontier from 2003-2004 and 2013-2014 for some industries (20 and four) can be because of errors in pronounced records.   Table 5 a value over 1 means progress, less than 1 means regress, and equal to 1 means no change. (b) Average geometrically of the sample (GE). Table 6 presents calculated technical progress/regress as measured by average shifts in the industry frontier from period t to period t + 1. This corresponds to the term in the bracket in Equation (4) On the other hand, for more than half of the industries our calculation showed technical progress of more than 4% between 2007 and 2008. On average we found progress in five periods for the latter part of our study period.     Table 7 a value over 1 means progress, less than 1 means regress, and equal to 1 means no change. (f) Average geometrically of the sample (GE). Table 7 summarizes productivity change results in manufacturing industries, that is the evolution of Malmquist output-based productivity index in Equation (4), which is a combination of the efficiency and technical change components, that are discussed above. According to our results, we have had, on average, productivity gains in 13 periods and productivity losses in one period. Again, only three industries (manufacture of electric equipment (N • 19), other basic chemical industries (N • 23) and para-chemistry (N • 24)) showed progress in all periods. For all industries and all periods, we found productivity gains in 366 cases and productivity losses in 110 cases, i.e., progress in 77% of all cases. For the period 2011-2016 we found progress in 81% of all cases. We note that on average, progress in productivity during the five latter years of our study period is mainly explained by positive shifts of the frontier. Table 8 shows an annual total factor productivity growth of 2%; with technical change (or frontier-shift) contributing 3.1% per year and decline in efficiency change of 1.2%. We can say that during our study period, the increase of productivity is a result of technological progress. In terms of individual industry performance (see Table 9), the most spectacular performance is posted by manufacture of electric equipment (N • 19) with an average annual growth of 5.2% in TFP over the study period. Other industries with strong performance are, among others, pharmaceutical industry (N • 25) and manufacture of oils and other fatty substances (N • 4).  Table 9 shows the mean technical efficiency change, technical change and TFP change for the 34 industries over the period 2002 to 2016. In terms of individual industry performance, the most spectacular performance is posted by manufacture of electric equipment (N • 19) with an average annual growth of 5.2% in TFP, which is due to 5.2% growth in technical change over the study period. Other industries with strong performance are, among others, pharmaceutical industry (N • 25) and manufacture of oils and other fatty substances (N • 4). The unweighted average (across all industries) growth in TFP is 2%.
Construction materials, ceramic and glass industries (CMCGI); mechanical and electrical industries (MEI); and chemical industries (CHI) are the major performers with an annual TFP growth of 2.6% (mainly due to technical change growth of 3.2%, 3.9%, and 2.2%) followed by other manufacturing industries (OMI), agri-food industries (AFI), and textile, clothing, and leather industries (TCLI). Textile, clothing, and leather industries seem to be the weakest performer with only 1.3% growth in TFP followed by agri-food industries with 1.8% growth in TFP. A surprising result is that over the period 2002-2016, these results show that technical change is the principal source of TFP growth for all sectors as shown in Table 10.       For four sectors as shown in table 11: Other manufacturing industries (OMI); mechanical and electrical industries (MEI); textile, clothing, and leather industries (TCLI); and construction materials, ceramic, and glass industries (CMCGI), the long-run annual average rate of TFP, ranges For four sectors as shown in Table 11: Other manufacturing industries (OMI); mechanical and electrical industries (MEI); textile, clothing, and leather industries (TCLI); and construction materials, ceramic, and glass industries (CMCGI), the long-run annual average rate of TFP, ranges between 1.306% for textile, clothing, and leather industries and 3.355% for other manufacturing industries over the period 2002-2016. The situation is somewhat different for the two other sectors. In the chemical industries, TFP strongly increases by about 3.470% per year. But, the agri-food industries were characterized by lower rates (0.413%) over the study period.

Conclusions
In this paper the productivity growth in 34 Tunisian manufacturing industries over the 2002-2016 period within the framework of the DEA piecewise linear production function and the output-based Malmquist productivity index introduced by Caves, Christensen, and Diewert (1982) is analyzed. This allowed the simultaneous analysis of changes in best-practice due to frontier growth and changes in the relative efficiency of industry to movements towards existing frontiers. The results show that during our study period, the increase of productivity is a result of technological progress. In terms of individual industry performance, the most spectacular performance is posted by manufacture of electric equipment (N • 19). Other industries with strong performance are, among others, pharmaceutical industry (N • 25) and manufacture of oils and other fatty substances (N • 4). Considering the performance of various sectors, construction materials, ceramic, and glass industries (CMCGI); mechanical and electrical industries (MEI); and chemical industries (CHI) are the major performers. Textile, clothing, and leather industries seem to be the weakest performers.
The long run productive performance of Tunisian industries turns to be heterogeneous across sectors and sub-sectors. Some manufacturing activities experience a decline while others strengthen their position and contribute to modify the national production structure. However, these results suffer from a number of limitations. The main limitation is the lack of background or nondiscretionary elements into the study. This oversight is the outcome of insufficient facts and means, and it is difficult to comprehend why the variations in output, competence, and particularly technology, have occurred. Second, the measures of competence and scientific advancement delivered in this reading are best practice, in that the fabrication frontier is a derivative from the illustration itself. There is no information to propose that efficiency modification in manufacturing has not either been commendable nor equivalent to that observed in other manufacturing companies. Lastly, the current reading shares its deterministic appearance in common with other DEA-based methodologies; that is, no opening is made for capacity or condition fault. Nonetheless, the Malmquist index method is exclusively common and can also be instigated in econometric frontiers. This points out a significant space for future research.
Appendix A Table A1. Sample distribution per activities branch.

Sectors N • Activities Branch (Sub-Sectors)
Agri-food industries 1 Slaughter 2 Dairy Industries 3 Grain processing 4 Manufacture of oils and other fatty substances 5 Cannery 6 Sugars and sugar confectionery industry 7 Miscellaneous agri-food industries 8 Manufacture of drinks 9 Tobacco industry Construction materials, ceramic, and glass industries 10 Extraction and shaping of quarry products 11 Manufacture of cement and cement items 12 Ceramic industry 13 Glass industry Mechanical and electrical industries 14 The steel industry, metallurgy, and foundry 15 Working metal 16 Manufacture of industrial equipment and machines 17 Manufacture of motor vehicles and cycles 18 Construction and repair of transport equipment 19 Manufacture of electric equipment 20 Manufacture of electronic equipment 21 Manufacture of domestic appliances Paper, printing and publishing industry 33 Manufacture of plastic products 34 Miscellaneous industries